ABSTRACT
When we proved Euler’s formula for polyhedra in Chapter 13, we used a two-dimensional “map” of the polyhedron that had the same number of vertices and edges as the original polyhedron. We used regions in the plane to represent the faces of the polyhedron. This kind of map, or graph, is an object worthy of study in its own right. Graph theory is useful for solving many kinds of problems that can be more easily represented and understood by these two-dimensional diagrams. It has applications in physics, chemistry, computer science, and many areas of mathematics. Graph theory can serve as a mathematical model for any system that uses a binary operation. We begin this chapter with the basic definitions for graphs as well as some elementary and historical puzzles and problems that lead to deep results.
